Parallel universes and other possible worlds are currently much in vogue, as evinced by the films Sliding Doors and Possible Worlds. In science, these intriguing intuitions assume rigour through the many-worlds theory of quantum mechanics, and in philosophy through the possible-worlds theories of the Princeton professor David Lewis, who has died, aged 60, of complications from diabetes.

Lewis is most celebrated for his "modal realism", a theory which argues that possible worlds are not just a concept for explaining possibility and necessity, but as real as our own universe. He also produced outstandingly innovative theories on scientific laws, chance, probability, causation, the identity and functionalist theories of mind, (linguistic) convention and a vast range of other issues. Together, his ideas in different areas form a grand, all-embracing theory, and to his many devotees he ranks as one of the great metaphysicians in this, or perhaps any, era.

Born in Oberlin, Ohio, Lewis was an undergraduate at Swarthmore College, Pennsylvania, initially in chemistry. While spending a term at Oxford, he attended lectures by Gilbert Ryle, who had disputed the existence of the mind in his controversial book, The Concept Of Mind, and became so enthused that he changed to philosophy on returning to the US. After graduating in 1964, Lewis took a PhD at Harvard under the great Willard van Orman Quine (obituary, December 30 2000).

Even as a graduate, Lewis had enormous standing in the philosophical world. The much-debated theory that had replaced Ryle's analytic behaviourism argued that mental states will ultimately turn out to be nothing but physical processes in the brain, and JJC Smart, one of the initiators of this identity theory of mind, visited Harvard in the mid-1960s. "I taught David Lewis," he said afterwards, "or rather, David Lewis taught me," and in 1966, the year before obtaining his doctorate, Lewis produced the essay An Argument For The Identity Theory, which improved on Smart's position.

Typically, Lewis not only got to the nerve of the issue, but took it in a new direction. Trying to rebut the commonsensical dualist objection that surely "experiences are non-physical and physically inefficacious", he said that experiences should be (in fact, implicitly were) considered as the effects of certain stimuli and the causes of certain behaviour. Pain, for instance, is whatever causally links a certain sensory input (having your eyes gouged out, for instance) with behavioural output (screaming) and other mental states (urgent desire to be rid of the pain).

Neural science will eventually show this causal "whatever" to be a particular state in the brain, just as (Lewis wrote in his 1972 paper, Psychophysical And Theoretical Identifications) a detective who knows in detail the roles - but not the identities - of conspirators involved in a murder will ultimately be able to establish who exactly these conspirators are.

Simultaneously, Lewis was setting the agenda in other areas of philosophy. In 1966, Convention: A Philosophical Study (his rehashed thesis) broke new ground in the philosophy of language, in which it remains a seminal work. He became assistant professor at the University of California, Los Angeles, in the same year, associate professor at Princeton in 1970, and full professor there three years later.

In Counterfactuals (1973), and many articles before and after it, he was working out his controversial theory of modal realism, which is most fully expressed in On The Plurality Of Worlds (1986). Since Leibniz's formulation of the idea in the 17th century, philosophers had treated possible worlds as a purely conceptual notion useful for explaining concepts of possibility and necessity: anything that we can coherently conceive as possible can be called a possible world, but if something is necessarily true, then it is true in all possible worlds.

Lewis argued that possible worlds were not concepts, but real - existing in the same way as our universe does and no different from it except in the details of what happens there. "The inhabitants of other worlds may truly call their own worlds actual, if they mean by 'actual' what we do," just as "the inhabitants of other times may call their times 'present', if they mean by 'present' what we do". After all, "our present time is only one time among many". "Actual" is on a par with "I", "here" or "now"; what it refers to depends on who says it and the world at which (Lewis's terminology) it is said.

As for counterfactuals, which appeal to what might have been, the counterfactual "If he hadn't pressed the alarm, she would have been killed," for instance, is true if there is a possible world in which he didn't press the alarm, and she was killed, that is more similar to our own world than one in which he pulled the cord and she wasn't killed. Of course, the person who was killed is only a counterpart to her equivalent in the actual world, even if both play similar roles in each of their worlds. And there is no spatial, temporal or causal connection between possible worlds and our own.

To postulate the reality of possible worlds is to spin metaphysics out of logic, and when Lewis spoke about it he usually met with "an incredulous stare" - this expression became a philosophical joke and the name of a section of On The Plurality Of Worlds. Yet it was, he said, the only way to make sense of everything.

Soon incredulity gave way to a cottage industry of objections and interpretations. For what possible worlds actually are (and virtually no one, perhaps not even Lewis, accepted their reality) does not affect the brilliant, sophisticated way he used them, analysing problematic notions in causation, universals, the content of thought, properties, probability, and the nature of propositions. Modal realism mowed down problems like a combine harvester (to paraphrase an admiring colleague) not only in philosophy, but in semantics, linguistics, game theory and economics.

Sometimes Lewis spoke as if he discovered his intentions, both practical and intellectual, almost by trial and error, and the same sort of induction seems to have occurred with his metaphysics. He said in the introduction to his Philosophical Papers Volume II (1986) that, like any analytic philosopher, he had set out to tackle problems piecemeal, but that he seemed almost inadvertently to have produced a coherent, unified thesis. This, which he called "Humean supervenience", says that the world is a "vast mosaic" of tiny facts and, at any instant, what it is, and what we can truly say about it, depends upon the patterns that these exemplify, just as in a pointillist picture what is depicted is determined by the dots.

Nothing that happens at one point logically fixes what happens at any other point, but it is the totality of what happens that fixes everything else. All Lewis's theories seemed to converge in this thesis, he said, but he admitted that there was a bug in the system - chance - which could subvert the whole thing. This was a problem he was still struggling with at the last.

Lewis expressed his esoteric ideas in brisk, sturdy, lucid prose, whether on paper or orally, but he was famously incapable of small talk. Shy, pale and lengthily bearded, he was affectionately nicknamed Machine in the Ghost (turning Ryle's disparagement of dualism on its head). But he could be unflamboyantly funny, especially in print, and his philosophical examples are witty without facetiousness or self-congratulation (a famous article contrasted a Martian whose response to painful stimuli is the inflation of cavities in his feet with a madman whose reaction is indifference).

Lewis was astoundingly modest and unpompous for a successful philosopher, always ready to respond to criticism, and unfailingly generous to students. Perhaps his dislike of pretentiousness and convention led to his love of Australia. His contacts with the Australian theorists Jack Smart and David Armstrong led to a lasting connection with the country, where he became a huge philosophical figure. Almost every year he and his wife stayed there for two or three months, and he became an aficionado of Australian rules football (he was buried with the Essendon club's season ticket), and its Bush ballads, birds and trains.

English railways were his favourites, however; he would travel on them for the sake of the journey. His basement was occupied by a model railway set, which the privileged were also allowed to play with, and walls were knocked down to accommodate it. Asked why he did not have a credit card, he said he did not want to be in debt.

Lewis restored philosophical respectability to systematic metaphysics. Like Hume, he tried to reconcile a scientific conception of the world with how it actually appears to us. He called himself "a commonsensical fellow (except where unactualised possible worlds are concerned)". The paper he was last working on used possible worlds to link personal identity with immortality. This may not sound commonsensical, but it is poignant for the many people that loved him as a philosopher and as a man.

He is survived by his wife, Steffi.

·David Kellogg Lewis, philosopher, born September 28 1941; died October 14 2001.